#45
Top 50 Mistake
Forgetting to include radii in sector perimeter
"The Missing Radii"
The Mistake in Action
Find the perimeter of a sector with radius 6 cm and angle 60°.
Wrong: Perimeter = Arc length = $\frac{60}{360} \times 2\pi \times 6 = 2\pi = 6.28$ cm
Why It Happens
Students confuse arc length with sector perimeter, forgetting that a sector has two straight edges.
The Fix
The perimeter of a sector includes:
- The arc (curved edge)
- Two radii (straight edges)
$$\text{Perimeter} = \text{Arc length} + 2r$$
Arc length = $\frac{60}{360} \times 2\pi \times 6 = 2\pi$ cm
Perimeter = $2\pi + 2(6) = 2\pi + 12 = 18.28$ cm (3 s.f.)
Spot the Mistake
Can you identify where this student went wrong?
Sector perimeter
= Arc length = $2\pi$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: